Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationKepler's LawEasy2 minPYQ_2020

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A planet of mass $4$ times that of the earth spins about itself and completes one rotation is $96$ hours. The radius of a stationary satellite about this planet in comparisons to the radius of the geostationary orbit around the earth is

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Answer:

Solution:

$T = \frac{2 π r^{\frac{3}{2}}}{\sqrt{G M}}$

$\begin{array}{l} ∴ 24 = \frac{2 π r^{\frac{3}{2}}}{\sqrt{G M}} .......... (1) \\ 96 = \frac{2 π r_{1}^{\frac{3}{2}}}{\sqrt{G \times 4 M}} .......... (2) \\ d i v i d e (1) & (2) \\ \frac{96}{24} = \frac{1}{2} {(\frac{r_{1}}{r})}^{\frac{3}{2}} \end{array}$
$8 = {(\frac{r_{1}}{r})}^{\frac{3}{2}} \Rightarrow \frac{r_{1}}{r} = 4$

$r_{1} = 4 r$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:GravitationSubtopic:Kepler's Law

⏱ 2mℹ️ Source: PYQ_2020

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